As is witnessed by railway statistics, Level crossing (LC) safety has always been one of the major concerns for railway stakeholders. LC safety is an issue at the crossroads between technical aspects, operational procedures and human factors, making the search for effective solutions a challenging task. This paper deals with technical aspects related to LC safety. In particular, we carry out an analysis pertaining to the diagnosability of two main failure classes that can affect the protection system at automatic LCs. In the current study, a labeled Petri net behavioral model depicting the global system function, including both the normal operation and the faulty behavior, is first established. Petri net has been used as the modeling formalism mainly for its mathematical foundations and expressiveness capabilities. Using such a mathematical notation is highly recommended to deal with dependability issues in safety-critical systems, especially in railways. Based on the established model, different model-based approaches for the diagnosis of discrete event systems (DESs) will be brought into play to investigate the diagnosability of two considered failure classes, while the obtained results will be compared. In particular, a technique that we have established, which is based on on-the-fly and incremental analysis of the model state space shows interesting efficiency, making it possible to tackle the combinatorial explosion problem, which arises particularly when considering multi-track LCs. The originality of this technique w.r.t existing DES model-based diagnosis approaches is that, in general, a partial building/investigation of the state space suffices to decide diagnosability and build an online diagnoser. Findings pertaining to LC safety are drawn based on a thorough discussion of the obtained results. In particular we show how the diagnosability analysis outputs can be taken into account in the global LC risk assessment process.